Search upward for a file in lua?

How can I search upward from my cwd to find a file?

Essentially, I want the lua version of this question.

I want to use my .luacheckrc as a root project marker.

I'm using Lua 5.4 without luafilesystem.

I figured out a dumb version that can only find files (not folders) and doesn't canonicalize paths:

local function file_exists(path)
    local f = io.open(path, "r")
    if f then
        f:close()
        return true
    end
    return false
end

function find_file_upwards(filename, start_directory)
    assert(filename:sub(-1, -1) ~= '/', "Cannot find folders: Only files are supported.")
    assert(start_directory:sub(-1, -1) == '/', "Folder paths must end with slash: /")
    local dir = start_directory
    for i=1,1000 do
        local fpath = dir .. filename
        if file_exists(fpath) then
            return fpath
        end
        dir = dir .. "../"
    end
end

Probably should strip paths off instead of using a loop so it can stop when it hits the root of the filesystem instead of many pointless retries.